Functional equations involving means

被引：17

作者：

Daroczy, Z. ^{[1
]}

Lajko, K. ^{[1
]}

Lovas, R. L. ^{[1
]}

Maksa, G. Y. ^{[1
]}

Pales, Z. S. ^{[1
]}

机构：

[1] Univ Debrecen, Inst Math, H-4010 Debrecen, Hungary

来源：

ACTA MATHEMATICA HUNGARICA | 2007年 / 116卷 / 1-2期

关键词：

p-Wright affine function; Jensen-affine function; linear functional equation; biadditive function;

D O I：

10.1007/s10474-007-5296-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, the functional equation f (px + (1 - p)y) + f ( (1 - p)x + py) = f (x) + f (y), (x,y is an element of I) is considered, where 0 < p < 1 is a fixed parameter and f : I -> R is an unknown function. The equivalence of this and Jensen's functional equation is completely characterized in terms of the algebraic properties of the parameter p. As all application, solutions of certain functional equations involving four weighted arithmetic means are also determined.

引用

页码：79 / 87

页数：9

共 8 条

[1]

Daróczy Z, 2006, P AM MATH SOC, V134, P521

[2]

DAROCZY Z, 1961, ACTA SCI MATH SZEGED, V22, P31

[3]

GILANYI A, 2001, REAL ANAL EXCHANGE, V27, P485

[4]

Kuczma M, 1985, An introduction to the theory of functional equations and inequalities

[5]

Lajko K, 1998, PUBL MATH-DEBRECEN, V52, P507

[6]

MAKSA G, 1991, C R MATH REP ACAD SC, V13, P274

[7]

Szekelyhidi L., 1991, Convolution Type Functional Equations on Topological Abelian Groups

[8]

Wright E. M., 1954, Amer. Math. Monthly., V61, P620

← 1 →